Electric Power Generation from Earth’s Rotation through its Own Magnetic Field

We examine electric power generation from Earth’s rotation through its own nonrotating magnetic field (that component of the field symmetric about Earth’s rotation axis). There is a simple general proof that this is impossible. However, we identify a loophole in that proof and show that voltage can be continuously generated in a low-magnetic-Reynolds-number conductor rotating with Earth, provided magnetically permeable material is used to ensure $\text{curl}(\mathbf{v}\times {\mathbf{B}}_{\mathbf{0}})\ne \mathbf{0}$ within the conductor, where ${\mathbf{B}}_{\mathbf{0}}$ derives from the axially symmetric component of Earth’s magnetic flux density, and $\mathbf{v}$ is Earth’s rotation velocity at the conductor’s location. We solve the relevant equations for one laboratory realization, and from this solution, we predict the voltage magnitude and sign dependence on system dimensions and orientation relative to Earth’s rotation. The effect, which would be available nearly globally with no intermittency, requires testing and further examination to see if it can be scaled to practical emission-free power generation.

Figure 1

A magnetically permeable, low-$R_m$ cylindrical shell with inner and outer radii $a$ and $b$ and length $L$ is moving at velocity $\mathbf{v}=v\widehat{\mathbf{y}}$ through background fields ${\mathbf{B}}_{\infty }=B_{\infty }\widehat{\mathbf{x}}$ and ${\mathbf{E}}_{\infty }=0$. A rectangular current path $C$ with vertices $d$, $e$, $f$, $g$ is embedded in, and translating with, the shell. An emf is generated around $C$ according to Eq. (63). A digital voltmeter (DVM) measures half this emf between $d$ and $f$. $C$ lies in the plane $x=b\cos {\varphi }_0\equiv x_0$, with $|x_0|\ge a$. It has right-angle vertices at $d=(x_0,y_0,-l/2)$, $e=(x_0,y_0,l/2)$, $f=(x_0,-y_0,l/2)$, and $g=(x_0,-y_0,-l/2)$, where $y_0=b\sin {\varphi }_0$ and $l/2<L/2-a$.

Figure 2

Deviations in the $x$ component $B_x$ of the magnetic flux density [Eq. (59)] for the moving cylindrical shell from that for the stationary shell [Eq. (10)], relative to the flux density at infinity, for a shell made of MN60 material (see text) with $b=1\mathrm{cm}$. These results are for the $x_0=b/\sqrt{2}$ plane, with $(a/b)=1/\sqrt{2}$.

Figure 3

Deviations in the $y$ component $B_y$ of the magnetic flux density [Eq. (61)] for the moving cylindrical shell from that for the stationary shell [Eq. (10)], relative to the flux density at infinity, for a shell made of MN60 material (see text) with $b=1$ cm. These results are for the $y_0=b/\sqrt{2}$ plane, with $(a/b)=1/\sqrt{2}$.